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Smoothing sparse multinomial data using local polynomial fitting

1997; Taylor & Francis; Volume: 8; Issue: 2 Linguagem: Inglês

10.1080/10485259708832717

1048-5252

Marc Aerts, Ilse Augustyns, Paul Janssen,

Advanced Statistical Process Monitoring

To estimate cell probabilities for sparse multinomial data several smoothing techniques have been investigated. Here we propose local polynomial smoothers as estimators for the cell probabilities and we study their performance. For the mean sum of squared errors we obtain the optimal rate of convergence and we establish a central limit theorem. We show that local polynomial smoothers provide a nice alternative for already existing nonparametric estimators and we discuss interrelations. Some illustrations are also included.